I still don't understand your problem with positional adjutment beyond presentation, but let's talk about WAA. WAA does include all the same defensive calculations as WAR. There are pros and cons of using WAA that go beyond presentation. The main difference between WAA and WAR is playing time. An average player can keep accumulating WAR as long as he performs above replacement. On the other hand, this player will always be 0 WAA whether he has 100 PA or 10000 PA. This might be appealing in HoF or MVP discussions, but maybe less so in roster construction discussions or comparisons between players who are not great players. For Hall of Fame discussions, players with high but short peaks will rank better in WAA, whereas players with longer duration but lower peaks will rank better with WAR. I think it's worth looking at both.
For other discussions, the problem with WAA is that an average player who is actually a pretty valuable player will always be 0 wins no matter how much he plays. A player who has a great 50 PA before going down with a season ending injury will have a higher WAA than an average player with 600 PA. With WAR, the full-season, player will be about 2 whereas the 50 PA player will be between 0 and 1 which I think is more appropriate. That's one extreme example, but illustrations the potential problem with WAA in player evaluation.